Seismic exploration involves surveying subterranean geological media for hydrocarbon deposits. A survey typically involves deploying seismic sources and seismic sensors (receivers) at accessible locations such as sea water, ocean bottom, or land surface. The sources generate seismic waves, or vibrations in the earth's subsurface, which propagate into the geological medium. Variations in physical properties of the geological media affect the propagations of the seismic waves, changing their speed and direction of propagation, focusing, defocusing, spreading, scattering, refracting, reflecting, and other alterations.
Portions of the seismic waves reach the seismic sensors largely due to reflections at rock boundaries with sharp seismic propagation velocity and/or density changes. Some seismic sensors are sensitive to pressure changes (e.g., hydrophones), others to particle motion (e.g., geophones), and industrial surveys may deploy one type of sensor or both. In response to the detected seismic waves, the sensors generate corresponding electrical signals, known as traces, and record them in storage media as seismic data.
For example, when a seismic wave is incident upon a boundary between two adjacent layers of rock, a portion of the incident seismic wave may be reflected if there is a change in medium properties such as density or wave propagation velocity (hereinafter “velocity”) between the two adjacent layers. A portion of the seismic wave may also be refracted or transmitted into the adjacent medium. The amplitude of the reflection depends on the angle of incidence θ. Moreover, a difference in velocity between adjacent layers may give rise to a so-called “critical angle” beyond which no wave of a given mode will be transmitted into the adjacent medium. According to Snell's law, the critical angle θc is related to the velocities of the two layers by the following equation:
                                          sin            ⁢                                                  ⁢                          θ              c                                =                                    v              1                                      v              2                                      ,                            (        1        )            where υ1 is a velocity of the layer (the first medium) with the incident and reflected waves; υ2 is a velocity of the layer (the adjacent second medium). As the incidence angle increases from pre-critical to post-critical, the wave is no longer transmitted into the second medium, and the reflected wave exhibits a sharp phase transition versus incidence angle. The critical reflections are also accompanied by creation of head-waves or diving waves that propagate along the interface and refract back into the first medium.
Seismic exploration requires imaging of the subsurface using the seismic data. Seismic imaging requires an accurate velocity model of the geological medium. One type of seismic imaging is called seismic migration. One method for obtaining the velocity model for migration is called migration velocity analysis (MVA). Migration velocity analysis is often done iteratively, starting with an imperfect velocity model, and is often performed by a process called tomographic inversion. A symptom of the imperfect velocity is that the same subsurface reflector will be imaged at slightly different depth (mis-alignment of the image) with different source-receiver distance (e.g. offset) or incidence angle. Images at the same surface location with different offsets or incidence angles are called a common-image gather (CIG). One gather usually refers to single x-y location on the Earth's surface, but a trace of depth positions. The above mentioned mis-alignment, sometimes called residual moveout, can be picked and used as input for migration velocity analysis to improve the migration velocity model. Oftentimes the residual moveout is a smoothly varying curve with offset or angle. However, critical reflections give rise to a litany of problems, discussed in greater detail below. These problems, among others, make residual moveout picking for tomographic inversion of seismic data difficult. The conventional approach to dealing with data containing critical reflections is to remove (i.e. mute) those data from the imaging gathers that correspond to the near-critical and post-critical reflections. The removed data, however, may be valuable for creating high-resolution and high-velocity-contrast velocity models. As can be seen from Eq. (1), as the ratio in velocity between the first layer and the second layer gets larger, the critical angle decreases. Thus, at high-velocity-contrast boundaries (e.g., between sediment and salt), conventional approaches must mute data starting at a relatively small offset or angle, and therefore may not have sufficient offset range for detecting the residual moveout for adequate velocity analysis. For sediment-salt boundaries, the conventional approach has been to mute out entire top-of-salt reflections, not just the post-critical part of the reflections. This prevents the velocity analysis immediately above and near the top of salt, especially in regions lacking coherent reflectors immediately above salt.